Beats from a Chasing Sound Source and a Fleeing Observer

Problem Statement

In a windless, one-dimensional space, there is a sufficiently large stationary reflecting wall on the right. Along this line, a sound source emitting sound at frequency $f_0$f0​ in all directions is moving toward the wall (rightward) at speed $V_s$Vs​. Between the sound source and the wall, there is an observer moving in the same direction (rightward) at speed $V_o$Vo​.

The observer simultaneously receives the sound wave coming directly from the source and the sound wave reflected from the wall (arriving from the front). Find the number of beats per unit time (beat frequency) $\Delta f$Δf observed by the observer. Let the speed of sound be $V$V, and assume $V > V_s > V_o > 0$V>Vs​>Vo​>0.

Constraints

• Speed of sound $V = 340\text{ m/s}$V=340 m/s
• Speed of sound source $V_s = 20\text{ m/s}$Vs​=20 m/s
• Speed of observer $V_o = 5\text{ m/s}$Vo​=5 m/s
• Frequency of sound source $f_0 = 640\text{ Hz}$f0​=640 Hz

Input Format

Find the beat frequency $\Delta f$Δf in hertz ($\text{Hz}$Hz) and give the answer as a positive integer.